Safe implementations of supervisory commands

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Abstract
Two different types of control strategy used to safely implement supervisory commands of hybrid dynamical systems are compared. Both approaches considered switch between members of a family of control agents to ensure that constraints on the plant state are not violated at any time. The first approach is motivated by a hybrid system architecture outlined by Kohn and Nerode (1993) and uses a Fliess functional series of the plant's output to form a system of linear inequalities characterizing safe control inputs. Control signals are determined by solving a sequence of linear programs. The second approach is a model reference control approach to hybrid systems introduced by Lemmon and Bett (1996) and uses a known safe dynamical reference model to characterize the desired plant behaviour. The controller is determined by representing the resulting error dynamics as a linear parameter varying system and applying linear robust control techniques to enforce a bounded amplitude performance level. The fundamental results underlying each of the methods are derived; the approaches are compared with regard to their complexity, performance and sensitivity to modelling uncertainty. A numerical example is included for illustration.

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